Question

A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9\%$. The change in its angular speed is

• A. increases by 9%
• B. decreases by 9%
• C. increases by 6%
• D. decreases by 6%

Answer 1

Answer: (D)

In this case, angular momentum, $J=I\omega$
Taken, $v=1$
$v^{\prime }=1.09$
and $\Delta v=0.09$
$\Rightarrow \omega \propto \frac{1}{I}$
Bul $I\propto r^2$ and $\omega \propto v^{1/3}$
$\therefore \omega \propto \frac{1}{v^{2/3}}($ or $v^{-2/3})$
$\therefore$ Change in angular speed
$=\frac{\Delta \omega }{\omega }\times 100=-\frac{2}{3}\frac{\Delta v}{v}\times 100$
$=-\frac{2}{3}\times 0.03\times 100=-6\%$
So, angular speed will decrease with $6\%$.